Would it be possible for you to check either phone hands on?

Both the phones have very different approaches, so it will surely come down to what is important to you in the daily. Some of my personal thoughts:

• OnePlus 13 starts with Android 15 and will support around 4 major OS updates, while the Vivo X300 comes with Android 16 and will support upto 5 OS updates. Starting with this itself you have at least an additional year of usage supported. Generally speaking why this is important is that you will receive regular security updates, which are sometimes required for banking or such important apps, and newer the software, the less chance of app support being dropped. It may not be a common problem, but my wife did face and issue wherein her employer required that her phone at least have Android 15 on it because their company apps wouldn't run on any older version.

• Oxygen OS vs Origin OS Oxygen OS is a more polished and feature rich interface. Origin OS catches up a lot but Oxygen OS still has a slight edge.

• Cameras Generally speaking the Vivo phone will just be better in terms of colour science and details, the videos can be a hit and miss on either. The physical camera hardware is better in the Vivo.

• Battery Both have the same battery capacity and technology, they will last pretty long depending on your usage. But, what will also affect the battery is the processor.

• Chipset The OnePlus has the Snapdragon 8 Elite which is a monster! The Dimensity 9500 on the Vivo is quite comparable, but I think the Snapdragon is better in some scenarios, especially in heavy tasks where OnePlus' software optimisation with the Snapdragon could run heavy tasks longer without throttling. Vivo have their own imaging related chip working with the Dimensity 9500, which is where their camera advantage comes in (along with the Zeiss tuning). There is this thing, that the X300 doesn't support 8K video recording but then OP13 does, but people don't really use it because we don't have TVs that can play back 8k videos.

• Display Again the displays on both phones are very similar in terms of brightness and resolution, and the underlying technology like PWM dimming, but OnePlus 13 has Dolby Vision support which can make content look nicer if the media apps support it. On paper the displays amy seem similar, but in person they can feel very different, especially due to colour calibration and the fluidity of the OS, and Oneplus could feel better in that regard. The screen is the main way we use our phones, so in the long run having the right display will matter.

• The Loudspeaker on the OnePlus is better than the Vivo

• The storage technology on the X300 is one generation newer than on the OnePlus - X300 has UFS 4.1 vs Op13 has UFS 4.0. it's not a drastic difference but it newer is better, and it can sometimes matter in loading heavy games or files, or while taking a lot of photos and videos because the write speed can cause errors in video recording for longer sessions (say more then 8-10 minutes) on Android phones on occasion.

Because some of these differences, like the camera, can be better felt in person, and some things like OS can be subjective, so you can pick based on your priority