I have an original Winchester 1895 Takedown in 30-06. Have carried it in good weather for deer hunting, but have not dropped a deer with it yet.
I much prefer the 1895 over the BLR. Frankly, I think the BLR is just too ugly. The 1895 may not win any beauty contests, but I don't think it's ugly.
I don't have a Browning 1895, though I looked for a carbine in 30-06 before winding up with my Winchester. I'd still like to get a carbine in 30-06 or 30-40 US (Krag). A carbine has the wood top piece on the forend and a barrel band.
I have a Browning 1886 rifle and carbine, and they are well made. The Browning 1895s are no different, and I would not hesitate to get one.
The modern Winchester 1895 is made in the same factory as the Browning 1895, using the same tooling. It has a rebounding hammer and a tang safety. I hate tang safeties because they make installing a tang sight difficult, but the 1895 design really does not lend itself to using a tang sight, so this might be a moot point. If I could not find a Browning 1895 I would not turn down a modern Winchester 1895.
One real advantage the BLR has is that it can be readily scoped. The 1895 is not a design that works well with scopes. A peep sight is probably the best you can do with it. At one time I wanted a older BLR in 243 strictly for whacking coyotes, but have plenty of other guns to do that. A friend has killed a lot of coyotes with a 243 BLR. Another advantage is the BLR is available in a wider range of cartridges, including magnums. The 1895 advantage is it is an old west lever gun and is a transition model between big game rifles using large blackpowder cartridges and powerful smokeless cartridges. A timeless classic.
Either gun will serve you well, but if you don't need optics, I think the coolness factor of the 1895 far outweighs the BLR.