The US will lose a naval war, particularly early but any land armies GB sends to US shores is turned into hamburger. It can't possibly send and supply am army large enough to compete with what the US can raise.
But "Can raise" is the key, isn't it? The US
is going to need time to do this - less time than in 1888, say, but more than it took Britain in OTL WW1. (Because the US in 1895 has a standing army plus reserves of ~125,000 and the British in 1914 had a standing army plus reserves of 975,000.)
Basically the US mobilization curve is going to be near-as-makes-no-difference the curve from the Spanish American War, so we have that as a comparison. The bottom line is that by the time the US has a land army able to launch an offensive into Canada, say, the British have been dug in there for weeks or not months.
The British don't have the capability to conquer large swathes of the US, but they should be able to do substantial damage if any landed army is fairly early on.
Since the likely outcome of a war,
if there is one, is a phase of warfare which primarily serves to determine who's getting what at the peace table, then the most likely duration of the war is short - and, as such, I doubt the US can raise more than one field army of ~125,000 (National Guard plus regulars) with any depth to it.
That's about as large as the British would likely commit to the fight anyway (though they put much more into the Second Boer War), so it turns out quite even numbers-wise and training/equipment seems likely to decide any land clashes.
Training - the US force has the disadvantage of not being all regulars.
Equipment:
Rifles.
The British have the Lee-Metford and early Lee-Enfield. They're using smokeless powder on the Lee-Enfield, but not on the Lee-Metford.
Either way they have a crazy fast firing magazine rifle.
The US has the Springfield 1892, which is a bolt action rifle with notably slow loading.
This means the British probably have a slight advantage with the Enfield and a disadvantage with the Metford.
Artillery.
The US has at most 56 Hotchkiss guns and may have some Maxim pom-poms. (Can't tell.) Aside from that their artillery may actually be ACW vintage, which is scary... I'd appreciate being corrected. They also have Gatlings, and seem to have Hotchkiss machine guns.
The British have smokeless powder breechloaders (the Ordnance BL 15lber) but no pom-poms. Fortunately for them Maxim has a supply at the factory (OTL some were shipped out in a hurry during the Boer war.) The British also have many, many Maxims (a weapon the US army has not adopted) and some heavier artillery.
Looks like mostly a wash.
Overall conclusion:
The main problem the US has with any war in North America is that almost everyone's going to be inexperienced. Aside from that, they're pretty well off as far as equipment quality goes.
I think the most likely situation for land warfare is the US invading Canada to try and gain leverage, and the British and Canadians defending it. (This is going to be painful for the Americans.) There might also be small attacks where the British try to neutralize forts. (This is going to be painful for the British land troops.)
The naval side of things, OTOH, is basically Britain Rules the Waves. These are the days of the Royal Sovereigns, true battleships wearing steel armour and carrying rifled-breech-loaders firing smokeless explosive rounds.
