I'd bet on the shadows personally. Ancient + 20 scouts means more or less guarenteed -2 to stealth on all your ships, given shadow maneuverability and scout weapon ranges thats probably going to be another -1 so hes arlready looking at 2+ stealth rolls. And 20 scouts worth of firepower should kill/cripple a couple of sharlins in a turn with relative ease, in reaturn, you should be able to drop stealth on 3 or 4 of his ships and get maybe 3 kills on turn 1 but thats 3 scouts out of 20 gone compared to most likely 2 of your 4 ships.
If you play it well then you can mininimise things a bit but from where I'm sitting I'm afraid this is only going to end with 'Minbari got PWNED' syndrome

Good luck anyway though
To break things down a tad more:
Without Terrain/Hyperspace I see the game going, assuming no massive balls-ups by either side:
Turn 1 Shadows close as fast as they can, they WILL get in range but wont be able to avoid the Minbari foward arcs. The minbari will move forward as slowly as possible scrambling Nials with the Shadows, and will fire most liklely a couple of Sharlins to be SURE per shadow ship shadow ship and the Leshaths will most lilkely just move up normally, perhaps closing blast doors if theyre only going to get one arc on target anyway, but if the shadows are close enough Id turn em so I can use both froant and one side gun set, same goes for the sharlins for that matter.
Shadows have most liklely won initiative and thus will fire first. With 20 scouts they should easily be able to lower stealth and paint each sharlin but will most likely focus fire on one till it dies then move on to the next.
In return I'd expect 2 Scouts to get vaporised by a couple of sharlins beams each and the secondary firepower of all 8 Minbari ships should hapily toast a 3rd one. Alternately the Minbari could play it a bit riskier and try to pin 4 scouts with the Sharlins beams (but most likely wont kill all 4 if they do this) and fry a 5th one with seconadries.
The upshot is that as of the start of turn 2 I'd expect there to be 4 Leshaths and 2 Shadlins with about 10-12 Nials out facing off against around 16-17 Shadow scouts, 15-16 of which I'd expect to be undamaged. It's possible a third sharlin might have suffered damage too if the scouts had a good round of shooting.
Turn 2 I'd expect the Shadows to be able to avoid the main guns of the Minbari for the most part and to lose the remaining 2 sharlins this turn, the shadows in turn I'd expect to lose a further 2 -3 scouts to massive combined secondaries and Nial Gankage.
Turn 3 onwards I'd expect the shadows to MASSACRE the remaining leshaths for minimal losses and after all the ships are dealt with they can simply form an massive area covering each other which is pretty much instant death for any Nial flight that enters this area. Game over.
If the shadows play it right I'd wager you'll see the Minbari wiped out for the loss of about 10 shadow scouts. And thats without any Terrain or hyperspace. If there IS terrain and hyperspace I'm afraid that favours the shadows EVEN more strongly. If the Minbari are lucky, and play very well, AND the shadow player is, ahem, lets call it 'tacitcally challenged' to be polite... no actually forget being polite: 'if the shadow player is an idiot' then I could MAYBE envision the minbari pulling it off if hes mad enough to feed you his scouts piecemeal so you can take them out as they come but if he just keeps them together and swarms your fleet one by one then I dont see him winning but any other way the minbari are boned. no pun inended.