Is there a significant difference in weather conditions between the West and East side of the island of Phuket or do you have to go the East coast of the country for much better weather?
The weather on Phuket won't be significantly different according to which side of the island you are on. While it may indeed rain in one area and be sunny in another area, you have pretty much the same chance of getting rained on regardless of where you are on the island.
Regarding weather conditions on the east and west coasts of the Malay Peninsula (southern Thailand), below are some stats. I'd love to encourage you to come to Phuket for your honeymoon, but your decision may rest on what the deal breaker/deal maker is for you. If rainy weather is going to spoil your honeymoon, go to the Gulf. If diving is key and you plan to canoodle in your honeymoon suite when you're not on a dive boat, come to the Andaman.
Here are some weather stats from a couple of sources.
Source 1: Thai Meteorological Department
Phuket 30-year averages for September:
Minimum temperature = 23.9 C
Maximum temperature = 30.7 C
Rainfall = 399.0 mm
Rainy days = 23
Samui 30-year averages for September:
Minimum temperature = 24.9 C
Maximum temperature = 31.5 C
Rainfall = 113.2 mm
Rainy days = 16
Source 2: Weather4Travel:
Phuket (works for the Andaman coast in general--Phi Phi, Lanta, Krabi
September in Phuket
In September the average maximum daytime temperature in Phuket is a hot 31°C (87°F), with high heat and humidity, while the average minimum night-time temperature is a warm 24°C (75°F).
On average 398 mm (15.7 inches) of rainfall is expected in Phuket during September with rain generally falling on 19 days of the month. There are usually 5 hours of bright sunshine each day, which represents 43% of daylight hours.
During September around midday under clear sky conditions the UV Index in Phuket is Extreme (UV Index 11+). Average sea temperature around Phuket in September is a warm 29°C (84°F).
Samui
September in Ko Samui (works for Gulf islands of Samui, Tao, Pha Ngan
In September the average maximum daytime temperature in Ko Samui is a hot 31°C (87°F), with high heat and humidity, while the average minimum night-time temperature is a warm 24°C (74°F).
On average 141 mm (5.6 inches) of rainfall is expected in Ko Samui during September with rain generally falling on 18 days of the month. There are usually 6 hours of bright sunshine each day, which represents 46% of daylight hours.
During September around midday under clear sky conditions the UV Index in Ko Samui is Extreme (UV Index 11+). Average sea temperature around Ko Samui in September is a warm 29°C (84°F).
Having said that, on rainy days it rarely rains all day, but it may rain torrentially followed by bright sunshine. The rainwater is quite warm--nothing like the cold mist and drizzle you are used to at home. The biggest issue in terms of rainy season weather in Thailand for diving is the condition of the sea. Rain storms tend to create swells and surges that may make being on a boat uncomfortable.