I have a mini-dvd recorder. Like it, and it is far better than tape. It always resets itself to the last place it was recorded to, so you no longer have gaps in your recordings. Never record over what has already been recorded. I am sure you could do that if you wanted, like if you were making a specific tape, and wanted to do some editing. I am not that up on it, the wife uses it more than I do. For me I just want to record events, and I am not all that concerned with it being properly edited.
The biggest issue for me is that it doesn't have as much memory per DVD as you had with tapes, so you always need to have an extra or two with you, because you will always seem to run out of available space. Also you have to reformat (or something like reformat) to play in your DVD, so you cannot play on your TV until you are done recording on that DVD. I got mine 2-3 years ago, so the latest and greatest may have better features.