A speaker change may give some tonal & volume enhancement but you won't turn it into a gigging amp; it is what it is. The AD15VT-XL is a practice/small club amp with a 10" speaker (the equivalent AD15VT only had an 8" speaker).
As background, the XL's (Xtreme Lead) were brought out solely to meet demand (which turned out to be significantly over-estimated) in the US for higher gain models. Although the XL's had some following/supporters, ultimately lack-lustre sales meant that these were only in production for a relatively short time.
Two 15w amps with 100dB speakers - will give a wider, bigger sound but clean headroom & over all volume is still going to be limited & IMHO may still struggle in a mix. But it does depend on type of music & overall volume levels. There are some youtube clips of 15w Valvetronix amps on stage unmiked & they do surprisingly well.
I've recently replaced the stock Celestion Rocket 50 (95dB) in my all-valve class A/B Laney Cub 15w with a Celestion Vintage 30 (100dB). Big difference in tonal quality & volume (see my 'voxman5' channel on you-tube for demos) and I think it's definitely loud enough for rehearsals & maybe smaller gigs, but clean headroom will still be limited. As an all-valve amp its louder in real terms than a 15w Valvetronix and you'd likely need a 30w Valvetronix AD30VT, AD30VT-XL, VT30 or VT40+ to compete with it.
If you're going to gig without miking up to the PA, volume wise you're going to need at least a 50 watt amp. The boxiness you refer to is not the AD15VT-XL per-se, merely a symptom of any combo amp with a single speaker in a small cabinet. I have the latest VTX150 Pro on loan - very nice amp, very very loud, and great tone/versatility....but within the limits of a single 12" in a small cab, it too is boxy as compared to my 2x12" AD120VTX. A 1x12" extn cab is available for it (which I don't have) and that will make a huge difference. However, it will still lack the 'reinforcement' effect of 2 speakers in a single larger cab - it's just physics.
If you want a fuller, bigger tone for gigging (un-miked) IMHO you need a 2x12" amp. In the Valvetronix series these are: AD120VT/VTX, AD100VT, AD100VTH (head) plus cab, AD100VTXL, VT100, VT120+, or the new VTX150 Pro Neodymium (definitely loud enough on its own, but fuller tone & rated at 300w with the extn cab!).
Rich

"I started out with nothing ...and I've still got most of it left!" (Seasick Steve)