Why all the tough questions one asks? Some of the hardest are subjective and personal in nature for sure.
What are mirrorless and what is a DSLR? Well if you don’t know then it likely is not any concern which is best, so I will answer that maybe in another blog.
What are pros and cons of each?
Well for the low end consumer budget cameras, it is fairly safe to say that the mirrorless will win the race. For higher end cameras the answer is not so clear.
For viewfinders the DSLR with its pentaprism is still the sharpest and brightest view. That will eventually change likely but for now it has not and likely will be a while before it does.
For focus speed, normally DSLR and mirrorless used a different focus method. The Sony A7 which is a hybrid using both systems is one of the few which can give DSLRs a run for the money. However, generally speaking for fast moving targets/subjects a DSLR still reigns supreme in focus speed.
However in focus accuracy the mirrorless wins the race. At least initially, due to the way the DSLR focuses. For manual focus there is no difference and if one takes the time to fine tune their lenses with a DSLR this difference can be minimized or eliminated all together.
For size, the mirrorless will win almost every time, having smaller and lighter bodies. But, that lighter and smaller body may not work as well with the size of the lenses. Lens size is defined mostly by physics and making a smaller body does not reduce lens size (reducing the sensor can but that comes at other compromises as well). So you end up with a smaller and lighter camera body with a very large lens. Sometimes it may be okay, other times it may feel out of balance.
Shooting speed, there are some very fast DSLR cameras for shooting speed. The Nikon D500, a crop camera, can run at 10 fps for 200 shots without stopping.. one of the fastest in the industry for a crop camera. The Nikon D5, a full frame camera can run at high speeds as well. But the top mirrorless cameras can easily match these speeds, meaning shooting speeds are pretty much equal. When one gets a bit faster than the other it means little once you are at 10fps, the additional speed is of little value for most sports or bird photography (perhaps minor gains but the gains become less and less).
Battery life – the DSLR will win here every time – and it will likely be a while, if ever that the mirrorless can catch up.
Sony pretty much rules in the mirrorless market, however Nikon has pretty much closed the gap with the Z6 & Z7 camera bodies. Having said that Nikon has clearly said that they are not competing with their top pro bodies with mirrorless, at least not really yet. And Sony has nothing to compete with the top pro cameras either, many in fact do not consider the Sony as top pro level (although many will argue that one). Canon has nothing in the top mirrorless (or top DSLR either for that matter). Sony owns top mirrorless (with Nikon pushing hard behind) and Nikon owns top DSLR spots. Now having said that they all are excellent cameras and all take excellent photos.
Enjoy what you have.