If Princip is captured and talks, then demands to Serbia are not based on "prejudice" but are relatively legitimate. In particular Russia can't back up Serbia if it is "proven" (not just alleged) that at least some parts of the government were involved in this plot. Also if FF not killed or even shot, then likely the AH demands on Serbia will be more focussed. Absent Russia backing Serbia the spiral that led to WWI at that time does not happen. The rivalries are still there, the Ottoman Empire is still the "sick old man of Europe" etc, so some sort of conflict occurring 1915-1925 is not unlikely.
IMHO a different "WWI" may see different players to some extent. If Germany realizes that the Schlieffen Plan is both unworkable, and will guarantee the UK coming in against them you could see them not attacking through Belgium. Absent the German attack on Belgium, very likely the UK does not get involved or certainly not right away - if Germany, as the attack develops, simply asks for transit rights through Belgium to parts of France they have occupied the Belgians may very well grant it, and this does not bring the UK in.
If the UK does not join in, then expect Italy to either stay with the Central Powers or remain neutral (perhaps leaning CP). Removal of the Italian Front makes life easier for AH - though not "better".
Lastly, a conflict between Germany/AH & Russia/France/Serbia will see the USA absolutely neutral, and selling to both sides (no British blockade & France can't really mount one) and in that case IMHO Germany will be very careful with submarine warfare not to piss off the USA. Also, US loans to France will not be on the scale as OTL as absent the UK French credit not so good, and there will be potentially more loans to Germany....
Lots of butterflies