I'll be answering this for SS NU. If you had another format in mind, please tell me so I can edit the answer.
Timid Nature is better for Inteleon
Timid Nature is better for Inteleon to let you outspeed fast Pokemon. Inteleon's niche in NU is being a fast wallbreaker / pivot that outspeeds already fast Pokemon such as Tauros, Starmie, and Salazzle. To do so, it needs Timid Nature, making its speed stat 372. Tauros has a speed stat of 356, Starmie has a speed stat of 361, and Salazzle has a speed stat of 366. If Inteleon uses Modest Nature, its speed will be 339, which would allow the mentioned Pokemon to outspeed and OHKO it. Inteleon utilizes a Choice Specs set, meaning it gets a special attack boost from Choice Specs. This means that Inteleon doesn't need to use Modest Nature. Even if you were to use a Focus Energy + Sniper set, Inteleon still uses Timid Nature, as you have critical hits with Sniper that makes your attacks more powerful. Here are the sets for reference:
Choice Specs
Inteleon @ Choice Specs
Ability: Torrent
EVs: 252 SpA / 4 SpD / 252 Spe
Timid Nature
- Hydro Pump
- Dark Pulse / Surf / Scald
- Ice Beam
- U-turn
Focus Energy + Sniper
Inteleon @ Scope Lens
Ability: Sniper
EVs: 252 SpA / 4 SpD / 252 Spe
Timid Nature
IVs: 0 Atk
- Focus Energy
- Snipe Shot
- Ice Beam
- Dark Pulse
I'd like to mention that the three Pokemon I mentioned use a +Speed Nature, as they need to be as fast as possible to eliminate anything slower than them. They also have ways to make their attacks stronger without using Adamant/Modest Nature. Tauros has Sheer Force + Life Orb, Starmie has Life Orb + Analytic, and Salazzle has Nasty Plot.
The only time Modest Nature is better than Timid Nature for Inteleon is if you were to use Choice Scarf Inteleon, as it will be quite fast with Choice Scarf. However, I advise you to not use Choice Scarf Inteleon, as you'll find out that Inteleon will struggle to revenge kill opposing Pokemon. Choice Scarf Inteleon also means you won't have a way to boost the power of Inteleon's attacks.
TL;DR Timid Nature is better for Inteleon as it allows you to outspeed already fast Pokemon such as Starmie, Tauros, and Salazzle. Using Modest Nature on the Choice Specs and Focus Energy set allows the mentioned Pokemon to outspeed and eliminate you, which isn't desirable. Modest Nature is better than Timid Nature only on Choice Scarf sets, but Choice Scarf Inteleon isn't that good of a set.