The sound of 300B's and 2A3's will vary with the specific tube used, the amp/circuit it's used in and the system the amp resides in. (I'm assuming we're talking about single-ended circuits, not push-pull, although both tubes have been used both ways.)
That said, the following generalizations are based on my listening experience with the AES SE-1 Sig which can use either, the Cary 300SEI, Cary 2A3 monoblocks and Bottlehead Paramour monoblocks.
Tubes used are:
300Bs - Valve Art
2A3 - generic Sino, Valve Art, Sovtek, RCA biplate and KR
300Bs have a very lush midrange, not terribly extended bass and treble. The midrange is gorgeous, sweet, luscious, romantic - some reviewers have described it as "psychedelic". If you're a sucker for female jazz vocals, this is your ticket to paradise. Bass definition and dynamics are okay, not fabulous.
The 2A3's as a group are more extended and flatter in response from bottom to top. Used with an appropriate speaker, (efficient, flat, relatively high impedance), 2A3 bass is astonishingly deep, articulate and agile. The midrange can be very fine to excellent, treble can be extended and airy to bright, depending on specific amp and tube.
The Cary 2A3 monoblocks, with the KRs, had the greatest power in the bass. A beautiful, very dynamic sound with the right speakers.
The AES SE-1, especially with the headphone option, which mine lacks, is an incredible place for Head-fi/wizers to get started on tube sound. With a choice of speakers or headphones, 300Bs or 2A3's, they offer a wide range of choices and sounds in one piece of gear.
The Bottlehead Paramour offers the best combination of characteristics for my ears. The parafeed transformer topology and 2A3s offer incredibly fast articulate sound top to bottom. The bass is very deep, fast and detailed, beating the AES SE-1 and lacking only the Cary monos' impact. (This with the stock transformers. What do you want from a $550 kit?) The midrange and treble are the best among the amps I've owned. I'm upgrading the "iron" (transformers, chokes) in mine to see how far it can go. Among the tubes I've used with these amps, the Sovteks sound the most powerful, but lack the mdrange and treble refinement of the Valve Art and old RCAs. The RCA's make the midrange spookily real on voices and acoustic instruments. The Valve Art tubes run down the middle in terms of sound, are inexpensive and highly enjoyable. (A pair is included stock in the Paramour kits.(