Scenario 1: Bowser at base vs Eggman with only 7 days of prep.
i'd give this to bowser since at base bowser has Super Strength, Super Speed, Invulnerability, Flight, Teleportation, Pyrokinesis, Sonic Roar, Shock wave stomp, his spiked shell and has the ability to summon minions, shoot Meteors, along with his dark magic powers in Electrokinesis, Terrakinesis, Reality Warping, Spatial Manipulation, Gravity Manipulation, and Warping time and space and turning inhabitants int objects. along with this bowser can change his size by using magic or eating meat. and even with the give prep time eggmans machines were never built super sturdy since even tails can destroy them with minimal effort.
Scenario 2: Bowser with EVERYTHING HE EVER HAD vs Eggman with a year of prep.
bowser curbstomps star rod, grand stars, dreamy bowser, shrowser, his entire army powered by power starts/grand stars, ect. even with a full year of prep time anything that eggman could of used (time eater, chaos,exc) have either been destroyed or don't work for him either way and again most of his machinery isn't to teribbly powerful or helpful in a battle even given the chaos emeralds. since eggman mainly used them to either A, cause earth quacks, or power a machine that could only crack the planet surface or B power a machine or being that either betrays him (chaos) or suffers from an overload (emerl going on a complete rampage and losing all self-control.)