It all depends on what you mean by "finer". If you mean better quality then that is really down to personal preference really, decided by what aspects of the saw such as size, TPI, handle design and even blade shape you prefer. If you are talking about making smoother faced kerfs left after you have sawn the rip that is much more down to how the ripsaw has been set up by you rather than by make and size.
The first aspect to consider is the TPI, a higher count will mean a smoother face to the saw cut but also mean that a lot less is removed with each stroke equalling a lot more elbow grease being needed to achieve the cut.
The second aspect that a lot of people don't realise is that the amount of "set" on the saw has a massive impact on the quality of the surface left after the sawing is done and on how easy it is to actually move the saw in the cut while using it.
The third aspect is probably the most important is is entirely controlled by you and that is technique, which only comes with practice.
So when you take all this into consideration as long as the saw blade itself is actually straight, then it doesn't matter really as to the make, model or size of the saw other than it be long enough to reach the other side of the board you want to rip. A high TPI on a wide set saw will not result in a much better finished face than a low TPI narrow set saw unless you have the technique to apply the advantages that either setup will provide.
I have cut veneers by hand that are 1/32" (0.7mm~) using a 6 tpi almost zero set 24" Diston D8. It was a slow slow and painful experience taking a lot of concentration and the application of the correct techniques, such as sawing from both sides and swapping every inch or so to ensure accuracy for thickness. I don't do it now as I made a frame saw which is much better suited for this purpose with a 12 TPI and narrow set blade sharpened to a Rip profile and hand set by me using the appropriate eclipse saw set. Oh the saw set is also important as they come in various styles you just have to figure which suites you best, if it is the Eclipse style then remember they come with different sizes of pin for a range of size of saw. Using the wrong one really does affect the shape of the tooth and where it curves into the set and can make a big difference as to how efficient and easy the sawcut will be.
hth