One could easily make a case for either. I do think they're the top two films in terms of the originality, tension and how it intertwines with the narrative. OHMSS, GE and maybe TLD might come next.
But as for which wins out between FYEO and TND... I'll break down my thoughts:
PTSThe helicopter sequence with the seeming return of Blofeld resonates given Bond has just visited Tracy's grave... but it's not as tense as what it could/should have been and I think it's due to how Blofeld is treat. The arms bazaar action on the Russian border economically sets the main events of the film in motion with a good balance of tension, inventiveness and fun. The swinging camera shots, the music punctuating the action and the ticking time bomb effect with the missile strike makes for an excellent opener that screams James Bond.
Winner: Tomorrow Never Dies.
Car ChaseRemote control technology was the next logical step for Q-Branch after the submersible Wet Nellie and it doesn't disappoint. The gadgets feel fresh, and it was a nice touch for Bond to drive over the tyre spikes but then he's equipped with the re-inflatable tyres. It really is a technical achievement in convincingly executing the car's tech. And of course, Backseat Driver underscoring the sequence amplifies the fun and wow factor... But I'm just so drawn to the 2CV chase to be honest. It might actually be my favourite car chase in the series. The stunt work is incredible, and I like how Bond has to rely on his wits in a less-than car. It ups the tension while still being fun. And with Remy Julienne's genius in his choreography, well, it's the cherry on top.
Winner: For Your Eyes Only.
The Secondary ChaseI'm going to compare the Runaway and the Bike Chase sequences in this one because they're executed in a similar fashion: that Bondian escalation where its begins as a simple chase but progresses with more danger and sometimes absurdity that always enhances the fun factor. This is the toughest one yet, in my opinion.
Both start off with a stunt from great heights: the ski jump which kickstarts the chase and Bond and Wai Lin rappel from Carver's building using his banner. Then its ski chase > through the restaurant > the bobsled run > and onto a roof. For TND, it's then a handcuffed Bond and Wai Lin fighting for control of the bike while evading pursuers > onto the roofs with an added helicopter in pursuit > jump onto a lower rooftop and rumbling balconies > the chopper turning its blades into a weapon.
Runaway's energy is genuinely pulse pounding whereas the bike chase feels ballsier and heavy. And yet both are thrilling to watch. In both instances, I feel the filmmakers found genuinely fresh ways to keep Bond in danger and demonstrate something we haven't seen before.
The slight edge goes to Tomorrow Never Dies, for the cultural element (the Saigon streets and rooftops add local colour) while the action serves to characterise not only Wai Lin but the dynamic between she and Bond. Spottiswoode's direction to tell both the actors they're the one who's in control was a brilliant move.
Winner: Tomorrow Never Dies.
The Big StuntThe HALO Jump is hugely impressive but I think that there are a few too many edits that detract from the true spectacle it could have been. That said, there's something in the fact it's treated so unceremoniously in the film - that it's just a necessity for Bond to slip in undetected. But the rock climbing sequence is truly one of the finest sequences in any Bond film. The tension and the set up is unparalleled and that shot of Bond falling and hanging by the rope is truly one of the most harrowing moments in any Bond film.
Winner: For Your Eyes Only
This ended up being longer than anticipated so stay tuned for Part 2.