I think today, you would be looking at dna evidence. However for that to happen dna would have had to be collected off victims at the time and objects and since the suspects are dead, dna would have to be drawn from dead relatives.
There was an attempt to do this from a shawl but it proved inconclusive. http://www.independent.co.uk/news/sc...o-9804325.html
You couldn't rely on a written confession as the cases of the Guildford 4 and Birmingham 6 have shown how unsafe these can be.
Policemen at the time had their suspicions but these revolved around suspects fitting a profile and being in the area at the time.
The proof they would have needed was for the suspect to be caught literally red handed but JTR proved elusive in the warren (even one of the policemen was called Warren) of streets, alleys, courtyards and dark corners in Whitechapel at the time.
So you are left with a series of competing theories for which best fits the evidence. Of course none of them are a complete fit and that is why proponents of competing theories knock them down.
It is made even harder by the lack of consensus over which murders can be attributed to JTR, so you have a pic 'n mix approach, collecting murders to fit in with your theory.
What you are left with is 'my guess is as good as yours' as no one can say it is right but then again no one can say it is wrong.
The biggest attraction for any Ripperologist is the fact that it is unsolved and any amateur sleuth
can pitch in and play detective and be 'the one' to finally solve this age old mystery that it appears even the police at the time couldn't solve.
The attraction for the film industry is likewise unmasking an unknown serial killer (usually in hat and cape)
in foggy old London town walking the streets and murdering and performing the most horrible and shocking mutilations on poor defenceless women.
However my favourite suspect has always been Tumblety as in addition to him being suggested by some policemen
as a suspect as he fitted the profile and was there at the time, the American press
picked up the story when he fled Britain.
However I am sure there will be new discoveries and theories and this gives life to Ripperology
and makes the case soooooo enduring.