Hi @Jaeger
So I get it that you are at war with Tuscany and Savoy, and that you can barely win defensive fights despite having an extra 5k men in your army and being ahead by one mil tech. Now there are a few things you did not mention which also have a significant impact on the performance of your army:
[spoiler=List of modifiers that can also affect your army performance]Terrain and river crossing
Discipline
Military tactics (normally we treat it as the second "discipline" stat)
Power Projection (affects morale)
Army professionalism and drill (treat it as if it's discipline)
Military advisors (affects either morale or discipline but not both the same time)
Army composition
Unit selection (fire, shock and morale pips)
Combat width
Dice rolls[/spoiler]
Since @lordraphael beats me to this thread, I will just write down a few things that he did not mention in detail.
The year is 1530 so I would assume you just got mil tech 11 unlocked. Now, aside from giving you a small edge on some rather useless early inf shock and cav fire pip modifiers, the +2 combat width is probably the best thing mil tech 11 can offer in terms of winning battles. The increase in combat width from 25 to 27 means that you can put two extra regiments to fight on the first row and have one of them flanking the enemy on each flank.
Since we just mentioned about combat width, let's talk about it first. Combat width restricts the number of regiments that can be put into a direct fight in each battle phase. Numbers do not matter too much when the total number of inf and cav regiments exceeds the combat width, as some of the regiments can only wait in the second row. In this case, I can probably safely assume that you have about 5k extra reserves in each battle than Savoy and Tuscany. That means you were actually fighting with more or less equal numbers in each battle, and so other factors kick in.
Perhaps I should clarify that none of the three countries can really gain a slight advantage in land battles from national ideas. As for naval warfare, you should have a dominating position over the other two, but let's not get sidetracked there.
Idea-wise, defensive and quantity ideas are more important in the early game when it comes to waging wars (although aristocratic/plutocratic ideas are also good for certain countries/play-styles). If you know your manpower will most likely be above zero most of the time, then pick defensive ideas, just because it offers some juicy early-game advantage that scales well with greed, especially the yearly army tradition and morale bonus amongst other things. Plutocratic ideas can be a good replacement if you are still playing as a merchant republic as Venice and if you intend to play tall, just because the idea set offers some decent economic bonuses whilst still giving you the most crucial early-game military ideas, namely morale bonus and manpower recovery speed (you should have the first military idea set completed at around mil tech 10 or 11). Since you are Venice, you probably will want to do naval ideas. What I will say about naval ideas is that they aren't exactly that good in the game unless you can stack with your national ideas, like GB or Venice, so it might be worth it for some maritime/colonial empires.
Generals can be a deciding factor throughout the game, and it depends on your army tradition, military ideas and a bit of luck (some national ideas and ruler traits also offer bonus to certain pips of generals, but none in this case). Army tradition decides on the range of the amount of pips a general can have, so the higher the number, the higher chance your new generals will have more pips. As for military ideas, offensive ideas offer extra shock and fire pips to your new generals, whilst one of the defensive ideas gives your new general an extra manoeuvre pip (and let's just ignore siege pip here for the sake of discussion). In early game, you will definitely want to get a general with decent shock and manoeuvre pips to combine with the early-game cav advantage; whilst a general with better fire pips will come in useful in mid-to-late game as cav scales poorly unless you are playing a few certain countries where you get shocking bonus for cav. combat (pun intended; Poland/Commonwealth, I am looking at you 
).
Morale and discipline are equally important, but more so for morale in early game. The higher the morale, the more bodies you can throw into a single fight before you are forced to retreat due to insufficient morale; but discipline (and army quality) will have an edge in combat in late-game - it is better off to dishing out damage in each phase when combat width becomes a more limiting factor. That is the general rule of thumb, but there is an exception. If you have a cav-heavy army composition, then the extra discipline is usually better off than the morale bonus. With a bit of luck, you can stack-wipe an army of equal size in favourable terrain (enjoy doing that with the horde nations and late-game commonblob).
Military tactics is just as important as discipline, and you will want to make sure you are not far behind on that. As for military advisors and events, they will provide extra discipline or morale, and sometimes other military bonus like army professionalism or army tradition, and siege ability or fort defense depending on the idea sets that you choose and some luck, so choose them wisely according to the situation. It is necessary to adapt.
On certain tech levels, there are often a few choices you can choose for your new upgraded units. Usually, for inf units, we compare them with morale pips first, then fire pips, and shock pips at last. As for cav, it's usually the other way round. As for artillery, always go for the one with most fire pips, then onto shock. If you are being outnumbered, you will want to have more defensive pips for inf and cav units, and vice versa; but the choice for artillery should always be the one with most offensive fire and shock pips because that's how they can dish out the most damage in the back-rank.
As for terrain, army composition, dice rolls and other stuff that I didn't mention, raphael has explained more or less everything already, so I will just skip those. Just that if you are playing as a horde or the commonblob, you might want to consider a cav-heavy composition, but make sure the number of cav regiments stays within the healthy ratio.
That's more or less about it. I hope I haven't missed anything else that's important, because I am quite certain to have missed a bunch of core info that is well hidden inside my muscle memory. Anyway, please feel free to ask for further advice. 
